How do you find the conjugate of a beam?
Conjugate beam is defined as the imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI. The conjugate-beam method is an engineering method to derive the slope and displacement of a beam.
What is the use of conjugate beam method over other methods?
The conjugate beam method takes advantage of the similarity of the relationship among load, shear force, and bending moment, as well as among curvature, slope, and deflection derived in previous chapters and presented in Table 7.2.
When Macaulay’s method is preferred?
Macaulay’s method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay’s technique is very convenient for cases of discontinuous and/or discrete loading.
What is EI in conjugate beam method?
Conjugate beam method is the modified moment–area method. This method is based on the construction of a conjugate beam, defined as an imaginary beam of length equal to that of the original beam and loaded with an elastic weight M/EI, where M is the BM of the actual beam.
How many fixed joint will be there in a conjugate beam?
two fixed joints
How many fixed joint will be there in conjugate beam? Explanation: Since there are 2 fixed ends in initial beam, there will be two fixed joints.
What is difference between real beam and conjugate beam?
A comparison of two set of equations indicates that if M / EI is the loading on an imaginary beam, the resulting shear and moment in the beam are the slope and displacement of the real beam, respectively. The imaginary beam is called as the “ conjugate beam ” and has the same length as the original beam.
Where is Macaulay’s method used?
Which type of bending moment is taken as positive in continuous beams?
When a reinforced concrete continuous beam or frame beam is being considered, the positive bending moment occurs in the middle part of the span and the negative bending moment occurs near the support.
What is M EI diagram?
Procedure for Analysis If there are mixed with distributed loads and concentrated, the moment diagram (M/EI) will results parabolic curves, cubic, etc. Then, assume and draw the deflection shape of the structure by looking at M/EI diagram.
Which is an example of the conjugate beam method?
T he Conjugate Beam Method is another way of solving the deflection for beams. This post shows an example on how to apply it. We shall use the same beam example in the area moment method to see the differences between the two methods.
What’s the difference between area moment and conjugate beam?
We shall use the same beam example in the area moment method to see the differences between the two methods. For this beam example, let’s say we are interested in finding the deflections at every key point of the beam (A, B, C, D, and E) using the conjugate beam method.
How many deflections are there in a conjugate beam?
For this beam example, let’s say we are interested in finding the deflections at every key point of the beam (A, B, C, D, and E) using the conjugate beam method. This means we have to find 15 deflection components (3 for every position).
How are curvatures treated in the conjugate beam?
In the conjugate beam, the curvatures from the curvature diagram of the real beam are treated as distributed loads and the support conditions are converted as discussed in the previous section and shown in Figure 5.10.